A uniform solid sphere of radius R produces a gravitational acceleration of `a_g` on its surface. At what distance from the sphere's center are there points (a) inside and (b) outside the sphere where the gravitational acceleration is `a_g`/2?

Explanation

To solve the problem, we need to find the points where the gravitational acceleration is half of the gravitational acceleration at the surface of a uniform solid sphere. Let's denote the gravitational acceleration at the surface of the sphere as \( a_g \).

### Step 1: Gravitational acceleration at the surface
The gravitational acceleration at the surface of a uniform solid sphere is given by:
\[ a_g = \frac{G M}{R^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the sphere, and \( R \) is the radius of the sphere.
...